Step-by-step explanation:
45% of number = 180
=> 100% of number = 180 * (100/45) = 400.
Hence the number is 400.
The volume of the single crayon is 89.5 cm³, then the total volume of the crayons will be 2148 cm³. Then the correct option is D.
<h3>What is Geometry?</h3>
It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
A Crayon is shown here.
There are 24 crayons in a box.
The approximate total volume of the crayons will be
Total Volume of crayons = 24 × volume of the single crayon
The crayon is the combination of the cone and the cylinder
Then the volume of the single crayon (V₁) will be
Then the Total volume will be
Total volume = 24 × 89.5
Total volume = 2148 cm³
More about the geometry link is given below.
brainly.com/question/7558603
#SPJ1
This is quite a complex problem. I wrote out a really nice solution but I can't work out how to put it on the website as the app is very poorly made. Still, I'll just have to type it all in...
Okay so you need to use a technique called logarithmic differentiation. It seems quite unnatural to start with but the result is very impressive.
Let y = (x+8)^(3x)
Take the natural log of both sides:
ln(y) = ln((x+8)^(3x))
By laws of logarithms, this can be rearranged:
ln(y) = 3xln(x+8)
Next, differentiate both sides. By implicit differentiation:
d/dx(ln(y)) = 1/y dy/dx
The right hand side is harder to differentiate. Using the substitution u = 3x and v = ln(x+8):
d/dx(3xln(x+8)) = d/dx(uv)
du/dx = 3
Finding dv/dx is harder, and involves the chain rule. Let a = x+ 8:
v = ln(a)
da/dx = 1
dv/da = 1/a
By chain rule:
dv/dx = dv/da * da/dx = 1/a = 1/(x+8)
Finally, use the product rule:
d/dx(uv) = u * dv/dx + v * du/dx = 3x/(x+8) + 3ln(x+8)
This overall produces the equation:
1/y * dy/dx = 3x/(x+8) + 3ln(x+8)
We want to solve for dy/dx, achievable by multiplying both sides by y:
dy/dx = y(3x/(x+8) + 3ln(x+8))
Since we know y = (x+8)^(3x):
dy/dx = ((x+8)^(3x))(3x/(x+8) + 3ln(x+8))
Neatening this up a bit, we factorise out 3/(x+8):
dy/dx = (3(x+8)^(3x-1))(x + (x+8)ln(x+8))
Well wasn't that a marathon? It's a nightmare typing that in, I hope you can follow all the steps.
I hope this helped you :)
